I used to wear just the wrap around clear plastic safety glasses, until I got a piece of steel in my eye while grinding. No damage done but it made me think twice. I now wear the clear plastic shop goggles, that completely cover my eyes, underneath, top and sides. I haven't had any trouble with anything getting in my eyes except sweat now!
I keep bricks in front of the door of my gasser and tend not to stare into the fire much, so I haven't been too worried about IR damage. I will still look into getting something though, I want to continue to see until I'm no longer seen by anyone!